The Dutch striker spent eight years with the Gunners before heading to Old Trafford in the summer of 2012.
His first season with United saw him land the Premier League Golden Boot as he collected a first title winners' medal.
The 2013/14 campaign has started a little slower than Van Persie and the Red Devils would have liked, with table-topping Arsenal having edged eight points into the distance.
United will get the opportunity to close that gap during a home date with the Londoners on Sunday, and Moyes insists Van Persie will not be casting any envious glances in the direction of the visitors.
He said in The People: "Robin must have had strong views about joining Manchester United and I'm sure he'd say he's made the right choice.
"He was a great player at Arsenal. What he did there was great and he's come to Manchester United and done exactly the same.
"Nobody wants to let their best players leave and Robin, undoubtedly, was one of Arsenal's best players.
"But his contract was running out, so there was a situation where Arsenal had to act and United wanted him."